Enhancing the implantation of mechanical circulatory support devices using computational simulations

Introduction: Patients with end-stage heart failure (HF) may need mechanical circulatory support such as a left ventricular assist device (LVAD). However, there are a range of complications associated with LVAD including aortic regurgitation (AR) and thrombus formation. This study assesses whether the risk of developing aortic conditions can be minimised by optimising LVAD implantation technique. Methods: In this work, we evaluate the aortic flow patterns produced under different geometrical parameters for the anastomosis of the outflow graft (OG) to the aorta using computational fluid dynamics (CFD). A three-dimensional aortic model is created and the HeartMate III OG positioning is simulated by modifying (i) the distance from the anatomic ventriculo-arterial junction (AVJ) to the OG, (ii) the cardinal position around the aorta, and (iii) the angle between the aorta and the OG. The continuous LVAD flow and the remnant native cardiac cycle are used as inlet boundaries and the three-element Windkessel model is applied at the pressure outlets. Results: The analysis quantifies the impact of OG positioning on different haemodynamic parameters, including velocity, wall shear stress (WSS), pressure, vorticity and turbulent kinetic energy (TKE). We find that WSS on the aortic root (AoR) is around two times lower when the OG is attached to the coronal side of the aorta using an angle of 45° ± 10° at a distance of 55 mm. Discussion: The results show that the OG placement may significantly influence the haemodynamic patterns, demonstrating the potential application of CFD for optimising OG positioning to minimise the risk of cardiovascular complications after LVAD implantation.

The flow rate and the pressure at the flow boundary are denoted by Q and P. The peripheral and distal resistances are represented by R & and R ' , C is the compliance of the vessel, and P ()* is the pressure at the exit of the Windkessel model, specified initially as zero.The variables are defined in global parameters.
The original equation can be rearranged, the pressure time derivative term can be approximated as a forward Euler finite difference, and the flow rate time derivative can be estimated as a backward difference using surface average reports and field history monitors for the volume flow rate and pressure.
The solution is first order accurate and can be used to determine the pressure at the outlet of each artery.
The values RCR can be calculated relating the haemodynamic parameters to a circuit in parallel (Supplementary Figure 1) where the proximal resistance is related to a viscosity resistance, the distal resistance is related to the resistance of capillaries and veins, and the capacitor is equivalent to the vessel compliance.
In a parallel circuit, the following relations can be applied to the aorta and its arteries.

Total Resistance or Systemic Vascular Resistance
The cardiac output (CO) is the volume of blood pumped by each ventricle in 1 minute and is defined by the product of the Stroke Volume (SV), the volume of blood ejected from the ventricle with each beat, and the Heart Rate (HR), the number of times the heart beats per minute.

𝐶𝑂 = 𝑆𝑉 * 𝐻𝑅
Mean arterial pressure (MAP) is the average pressure in the arteries.This value is closer to value for diastolic pressure than systolic pressure because diastole lasts much longer than systole (Brzezinski, 1990).
The pulse pressure (PP) is the difference between the systolic and the diastolic pressures.It represents the pressure increase in the vessels created by ventricular contraction.Pulse pressure declines to virtually zero by the time it reaches the capillaries.

Outlets Resistance
There are two methods to estimate the outlet resistance: through the aortic 3D model and using percentages of flow from clinical documentation (Infantino, 2020).
The aortic 3D model is used to estimate the areas of the boundary outlets assuming that the outlets of higher area will have less resistance to the blood flow than the smaller outlets.

Peripheral Resistance
The pulse wave velocity (PWV) is used as an indicator of arterial distensibility, which is the ability of the arteries to expand and contract with the cardiac pulsation.Patients' normotensives and hypertensives with a similar mean age recorded their PWV with a continuous doppler unit coupled with an electrocardiogram and found that the carotid-femoral PWV is positively correlated to MAP (O'Rourke, 1995).The peripheral resistance in the boundary outlet is calculated in function of PWV and the density of the blood, ρ.

Total Compliance
The aortic compliance can be calculated in function of SV and the PP or using the graph of pressure and the decay time of diastolic aortic pressure,  (Westerhof et al., 2019).

Outlets Compliance
Assuming that the arteries outlets of higher area will have more compliance to the blood flow:

Wall Treatment for the Reynolds-Averaged Turbulence Models
A wall treatment is a set of near-wall modelling presumptions for calculating the effect of the turbulent velocity fluctuations on the averaged flow.Star CCM+ provides different wall treatments, depending on the turbulence model (Supplementary Figure 2).All-y + and two-layer all-y + models were used as wall treatment of the turbulence model on the transitional flow.The two-layer all-y + is recommended in flows where boundary layers play an important role.This applies to the aorta where the boundary layer is very thin and the vessel wall is moving radially (Febina et al., 2018).

Mesh Validation
Supplementary Figure 3. Volume flow rate comparison with 4D flow data.
Table 1 shows a close agreement, considering that the 4D flow estimated values already have a margin of error introduced by the intra-voxel velocity distribution and partial volume effects as well as noise and data manipulation (Rothenberger et al., 2022).There is a slight variation in the quantities of wall shear stress as, while all the curves follow the same tendency, changes are observed at the peak systolic for the maximum values of WSS where a convergence study is executed.

Turbulent Model Comparison Results
The two-equations turbulence models were simulated: realizable k−ε two-layer, Standard (Wilcox) k−ω, and SST (Menter) k−ω with its respective wall treatment.The results of the simulation are compared with the averaged volume flow rate values obtained from the 4D flow in three different aortic sections (Supplementary Figure 3).

Table 2 .
Averaged volume flow rate comparison of unstructured mesh in different aortic sections.
Supplementary Figure4.Wall shear stress comparison with the different meshes.